Is it harmful to mix houshold bleach to your bath water? And if so how can it affect you?

Whoa whoa bleach? Your skin is acidic and bleach is an extremely strong base.

It may cause a bad burning sensation and if you get it inside you it can be very poisionus. Further more the tip of your penis would burn very badly if it was submerged in this.
AND to top that off it would burn your eyes and if enough bleach got in your eyes pain wouldn't be the only problem you could go blind.

Stay away from this seems like a recipe for disaster.

First why ? Yes it will cause burns on your body

There is no medical or health reason to do this

Bleach quickly 'defats' the natural oils on your skin, and then proceeds to burn. The slippery feeling you first feel when you get bleach on your hands is the defatting process.

Household bleach is only concentrated by about 3 - 8%, and there is also lye added. Although lye is often in soaps you bathe with, you don't mess with the combination, and you beware of contact with any other substance, not just ammonia (which with bleach can kill you).

To add, it also kills the normal flora on your body that actually keeps you from getting sick, so you are actually defeating the purpose by using bleach.